Question

Demonstrati ca:($\frac{2a}{ a^{2}-4 } - \frac{2}{a-2}+ \frac{1}{a+2}$):$\frac{a-6}{4(a+2)}= \frac{4}{a-2}$

Answer 1

$( \frac{2a}{a ^{2}-4 } - \frac{2}{a-2} + \frac{1}{a+2}) : \frac{a-6}{4(a+2)} = \frac{4}{a-2} \\ (\frac{2a}{(a-2)(a+2)} - \frac{2}{a-2} + \frac{1}{a+2}) : \frac{a-6}{4(a+2)} = \frac{4}{a-2} \\ \frac{2a - 2 (a+2) + a-2}{(a-2)(a+2)} * \frac{4(a+2)}{a-6} = \frac{4}{a-2} \\ \frac{2a -2a - 4 + a-2}{(a-2)(a+2)} * \frac{4(a+2)}{a-6} = \frac{4}{a-2} \\ \frac{a-6}{(a-2)(a+2)} * \frac{4(a+2)}{a-6} = \frac{4}{a-2} \\ \frac{4}{a-2} = \frac{4}{a-2}$